Physica D: Nonlinear Phenomena [SJR: 1.048] [H-I: 89] [3 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 0167-2789 Published by Elsevier [2801 journals] |
- Vortex nucleation in a dissipative variant of the nonlinear
Schrödinger equation under rotation- Abstract: Publication date: Available online 27 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): R. Carretero-González, P.G. Kevrekidis, T. Kolokolnikov
In the present work, we motivate and explore the dynamics of a dissipative variant of the nonlinear Schrödinger equation under the impact of external rotation. As in the well established Hamiltonian case, the rotation gives rise to the formation of vortices. We show, however, that the most unstable mode leading to this instability scales with an appropriate power of the chemical potential μ of the system, increasing proportionally to μ 2 / 3 . The precise form of the relevant formula, obtained through our asymptotic analysis, provides the most unstable mode as a function of the atomic density and the trap strength. We show how these unstable modes typically nucleate a large number of vortices in the periphery of the atomic cloud. However, through a pattern selection mechanism, prompted by symmetry-breaking, only few isolated vortices are pulled in sequentially from the periphery towards the bulk of the cloud resulting in highly symmetric stable vortex configurations with far fewer vortices than the original unstable mode. These results may be of relevance to the experimentally tractable realm of finite temperature atomic condensates.
PubDate: 2015-11-27T12:49:00Z
- Abstract: Publication date: Available online 27 November 2015
- Stirring a fluid at low Reynolds numbers: Hydrodynamic collective effects
of active proteins in biological cells- Abstract: Publication date: Available online 14 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Raymond Kapral, Alexander S. Mikhailov
Most of the proteins in the cell, including not only molecular motors and machines, but also enzymes, are active. When ATP or other substrates are supplied, these macromolecules cyclically change their conformations. Therefore, they mechanically stir the cytoplasm and nucleoplasm, so that non-thermal fluctuating flows are produced. As we have recently shown [PNAS 112, E3639 (2015)], stochastic advection by such flows might lead to substantial diffusion enhancement of particles inside a living cell. Additionally, when gradients in the concentrations of active particles or in the ATP/substrate supply are present, chemotaxis-like drift should take place. Here, the motion of passive tracers with various sizes in a mixture of different kinds of active proteins is analyzed. Moreover, effects of hydrodynamic interactions on the motion of active proteins are explored. Theoretical results are compared with available experimental data for ATP-dependent diffusion of natural and microinjected particles in biological cells.
PubDate: 2015-11-18T12:19:23Z
- Abstract: Publication date: Available online 14 November 2015
- Contact-based model for strategy updating and evolution of cooperation
- Abstract: Publication date: Available online 12 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Jianlei Zhang, Zengqiang Chen
To establish an available model for the astoundingly strategy decision process of players is not easy, sparking heated debate about the related strategy updating rules is intriguing. Models for evolutionary games have traditionally assumed that players imitate their successful partners by the comparison of respective payoffs, raising the question of what happens if the game information is not easily available. Focusing on this yet-unsolved case, the motivation behind the work presented here is to establish a novel model for the updating of states in a spatial population, by detouring the required payoffs in previous models and considering much more players’ contact patterns. It can be handy and understandable to employ switching probabilities for determining the microscopic dynamics of strategy evolution. Our results illuminate the conditions under which the steady coexistence of competing strategies is possible. These findings reveal that the evolutionary fate of the coexisting strategies can be calculated analytically, and provide novel hints for the resolution of cooperative dilemmas in a competitive context. We hope that our results have disclosed new explanations about the survival and coexistence of competing strategies in structured populations.
PubDate: 2015-11-14T12:15:33Z
- Abstract: Publication date: Available online 12 November 2015
- On degree-degree correlations in multilayer networks
- Abstract: Publication date: Available online 12 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Guilherme Ferraz de Arruda, Emanuele Cozzo, Yamir Moreno, Francisco A. Rodrigues
We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to weighted networks and provides information about correlations considering pairs of layers. By analyzing the multilayer representation of the airport transportation network, we show that contrasting results are obtained when the layers are analyzed independently or as an interconnected system. Finally, we study the impact of the level of assortativity and heterogeneity between layers on the spreading of diseases. Our results highlight the need of studying degree-degree correlations on multilayer systems, instead of on aggregated networks.
PubDate: 2015-11-14T12:15:33Z
- Abstract: Publication date: Available online 12 November 2015
- Erratum to “The Kuramoto model of coupled oscillators with a
bi-harmonic coupling function” [Physica D 289 (2014) 18–31]- Abstract: Publication date: 1 December 2015
Source:Physica D: Nonlinear Phenomena, Volume 313
Author(s): M. Komarov, A. Pikovsky
PubDate: 2015-11-10T11:59:12Z
- Abstract: Publication date: 1 December 2015
- Uniform modeling of bacterial colony patterns with varying nutrient and
substrate- Abstract: Publication date: Available online 10 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Deborah Schwarcz, Herbert Levine, Eshel Ben-Jacob, Gil Ariel
Bacteria develop complex patterns depending on growth condition. For example, Bacillus subtilisexhibit five different patterns depending on substrate hardness and nutrient concentration. We present a unified integro-differential model that reproduces the entire experimentally observed morphology diagram at varying nutrient concentrations and substrate hardness. The model allows a comprehensive and quantitative comparison between experimental and numerical variables and parameters, such as colony growth rate, nutrient concentration and diffusion constants. As a result, the role of the different physical mechanisms underlying and regulating the growth of the colony can be evaluated.
PubDate: 2015-11-10T11:59:12Z
- Abstract: Publication date: Available online 10 November 2015
- Modulation theory, dispersive shock waves and Gerald Beresford Whitham
- Abstract: Publication date: Available online 5 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): A.A. Minzoni, Noel F. Smyth
Gerald Beresford (GB) Whitham, FRS, (13th December, 1927 to 26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction-diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham’s classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.
PubDate: 2015-11-10T11:59:12Z
- Abstract: Publication date: Available online 5 November 2015
- Simple nonlinear models suggest variable star universality
- Abstract: Publication date: Available online 10 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): John F. Lindner, Vivek Kohar, Behnam Kia, Michael Hippke, John G. Learned, William L. Ditto
Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes “golden” stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near − 1.5 , suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.
PubDate: 2015-11-10T11:59:12Z
- Abstract: Publication date: Available online 10 November 2015
- Editorial Board
- Abstract: Publication date: 1 December 2015
Source:Physica D: Nonlinear Phenomena, Volume 313
PubDate: 2015-11-10T11:59:12Z
- Abstract: Publication date: 1 December 2015
- Polar rotation angle identifies elliptic islands in unsteady dynamical
systems- Abstract: Publication date: 1 February 2016
Source:Physica D: Nonlinear Phenomena, Volume 315
Author(s): Mohammad Farazmand, George Haller
We propose rotation inferred from the polar decomposition of the flow gradient as a diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical systems. We consider here two- and three-dimensional systems, in which polar rotation can be characterized by a single angle. For this polar rotation angle (PRA), we derive explicit formulas using the singular values and vectors of the flow gradient. We find that closed level sets of the PRA reveal elliptic islands in great detail, and singular level sets of the PRA uncover centers of such islands. Both features turn out to be objective (frame-invariant) for two-dimensional systems. We illustrate the diagnostic power of PRA for elliptic structures on several examples.
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: 1 February 2016
- Concentration profiles of actin-binding molecules in lamellipodia
- Abstract: Publication date: Available online 4 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Martin Falcke
Motile cells form lamellipodia in the direction of motion, which are flat membrane protrusions containing an actin filament network. The network flows rearward relative to the leading edge of the lamellipodium due to actin polymerization at the front. Thus, actin binding molecules are subject to transport towards the rear of the cell in the bound state and diffuse freely in the unbound state. We analyse this reaction-diffusion-advection process with respect to the concentration profiles of these species and provide an analytic approximation for them. Network flow may cause a depletion zone of actin binding molecules close to the leading edge. The existence of such zone depends on the free molecule concentration in the cell body, on the ratio of the diffusion length to the distance bound molecules travel rearward with the flow before dissociating, and the ratio of the diffusion length to the width of the region with network flow and actin binding. Our calculations suggest the existence of depletion zones for the F-actin cross-linkers filamin and α -actinin in fish keratocytes (and other cell types), which is in line with the small elastic moduli of the F-actin network close to the leading edge found in measurements of the force motile cells are able to exert.
Graphical abstract
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: Available online 4 November 2015
- Network bipartivity and the transportation efficiency of European
passenger airlines- Abstract: Publication date: Available online 4 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Ernesto Estrada, Jesús Gómez-Gardeñes
The analysis of the structural organization of the interaction network of a complex system is central to understand its functioning. Here, we focus on the analysis of the bipartivity of graphs. We first introduce a mathematical approach to quantify bipartivity and show its implementation in general and random graphs. Then, we tackle the analysis of the transportation networks of European airlines from the point of view of their bipartivity and observe significant differences between traditional and low cost carriers. Bipartivity shows also that alliances and major mergers of traditional airlines provide a way to reduce bipartivity which, in its turn, is closely related to an increase of the transportation efficiency.
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: Available online 4 November 2015
- Consensus dynamics on random rectangular graphs
- Abstract: Publication date: Available online 4 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Ernesto Estrada, Matthew Sheerin
A random rectangular graph (RRG) is a generalization of the random geometric graph (RGG) in which the nodes are embedded into a rectangle with side lengths a and b = 1 / a , instead of on a unit square [ 0 , 1 ] 2 . Two nodes are then connected if and only if they are separated at a Euclidean distance smaller than or equal to a certain threshold radius r . When a = 1 the RRG is identical to the RGG. Here we apply the consensus dynamics model to the RRG. Our main result is a lower bound for the time of consensus, i.e., the time at which the network reaches a global consensus state. To prove this result we need first to find an upper bound for the algebraic connectivity of the RRG, i.e., the second smallest eigenvalue of the combinatorial Laplacian of the graph. This bound is based on a tight lower bound found for the graph diameter. Our results prove that as the rectangle in which the nodes are embedded becomes more elongated, the RRG becomes a ’large-world’, i.e., the diameter grows to infinity, and a poorly-connected graph, i.e., the algebraic connectivity decays to zero. The main consequence of these findings is the proof that the time of consensus in RRGs grows to infinity as the rectangle become more elongated. In closing, consensus dynamics in RRGs strongly depend on the geometric characteristics of the embedding space, and reaching the consensus state becomes more difficult as the rectangle is more elongated.
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: Available online 4 November 2015
- On complex, curved trajectories in microtubule gliding
- Abstract: Publication date: Available online 4 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Pierre Gosselin, Hervé Mohrbach, Igor M. Kulić, Falko Ziebert
We study the dynamics of microtubules in gliding assays. These biofilaments are typically considered as purely semiflexible, hence their trajectories under the action of motors covering the substrate have been regarded so far as straight, modulo fluctuations. However, this is not always the case experimentally, where microtubules are known to move on large scale circles or spirals, or even display quite regular wavy trajectories and more complex dynamics. Incorporating recent experimental evidence for a (small) preferred curvature as well as the microtubules’ well established lattice twist into a dynamic model for microtubule gliding, we could reproduce both types of trajectories. Interestingly, as a function of the microtubules’ length we found length intervals of stable rings alternating with regions where wavy and more complex dynamics prevails. Finally, both types of dynamics (rings and waves) can be rationalized by considering simple limits of the full model.
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: Available online 4 November 2015
- Spatiotemporal dynamics of distributed synthetic genetic circuits
- Abstract: Publication date: Available online 3 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Oleg Kanakov, Tetyana Laptyeva, Lev Tsimring, Mikhail Ivanchenko
We propose and study models of two distributed synthetic gene circuits, toggle-switch and oscillator, each split between two cell strains and coupled via quorum-sensing signals. The distributed toggle switch relies on mutual repression of the two strains, and oscillator is comprised of two strains, one of which acts as an activator for another that in turn acts as a repressor. Distributed toggle switch can exhibit mobile fronts, switching the system from the weaker to the stronger spatially homogeneous state. The circuit can also act as a biosensor, with the switching front dynamics determined by the properties of an external signal. Distributed oscillator system displays another biosensor functionality: oscillations emerge once a small amount of one cell strain appears amid the other, present in abundance. Distribution of synthetic gene circuits among multiple strains allows one to reduce crosstalk among different parts of the overall system and also decrease the energetic burden of the synthetic circuit per cell, which may allow for enhanced functionality and viability of engineered cells.
PubDate: 2015-11-06T11:46:42Z
- Abstract: Publication date: Available online 3 November 2015
- Interplay between consensus and coherence in a model of interacting
opinions- Abstract: Publication date: Available online 30 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Federico Battiston, Andrea Cairoli, Vincenzo Nicosia, Adrian Baule, Vito Latora
The formation of agents’ opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand, the concurrent participation of agents to discussions on different topics induces each agent to develop a coherent set of opinions across all the topics in which he is active. Moreover, the prevasive action of external stimuli, such as mass media, pulls the entire population towards a specific configuration of opinions on different topics. Here we propose a model in which agents with interrelated opinions, interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhood, strive to maintain internal coherence, due to the fact that each agent identifies meaningful relationships among its opinions on the different topics, and are at the same time subject to external fields, resembling the pressure of mass media. We show that the presence of heterogeneity in the internal coupling assigned by agents to their different opinions allows to obtain states with mixed levels of consensus, still ensuring that all the agents attain a coherent set of opinions. Furthermore, we show that all the observed features of the model are preserved in the presence of thermal noise up to a critical temperature, after which global consensus is no longer attainable. This suggests the relevance of our results for real social systems, where noise is inevitably present in the form of information uncertainty and misunderstandings. The model also demonstrates how mass media can be effectively used to favour the propagation of a chosen set of opinions, thus polarising the consensus of an entire population.
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 30 October 2015
- Asymptotic periodicity in networks of degrade-and-fire oscillators
- Abstract: Publication date: Available online 31 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Alex Blumenthal, Bastien Fernandez
Networks of coupled degrade-and-fire (DF) oscillators are simple dynamical models of assemblies of interacting self-repressing genes. For mean-field interactions, which most mathematical studies have assumed so far, every trajectory must approach a periodic orbit. Moreover, asymptotic cluster distributions can be computed explicitly in terms of coupling intensity, and a massive collection of distributions collapses when this intensity passes a threshold. Here, we show that most of these dynamical features persist for an arbitrary coupling topology. In particular, we prove that, in any system of DF oscillators for which in and out coupling weights balance, trajectories with reasonable firing sequences must be asymptotically periodic, and periodic orbits are uniquely determined by their firing sequence. In addition to these structural results, illustrative examples are presented, for which the dynamics can be entirely described.
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 31 October 2015
- Erosion of synchronization: Coupling heterogeneity and network structure
- Abstract: Publication date: Available online 1 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Per Sebastian Skardal, Dane Taylor, Jie Sun, Alex Arenas
We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 1 November 2015
- Cascades in interdependent flow networks
- Abstract: Publication date: Available online 29 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Antonio Scala, Pier Giorgio De Sanctis Lucentini, Guido Caldarelli, Gregorio D’Agostino
In this manuscript, we investigate the abrupt breakdown behavior of coupled distribution grids under load growth. This scenario mimics the ever-increasing customer demand and the foreseen introduction of energy hubs interconnecting the different energy vectors. We extend an analytical model of cascading behavior due to line overloads to the case of interdependent networks and find evidence of first order transitions due to the long-range nature of the flows. Our results indicate that the foreseen increase in the couplings between the grids has two competing effects: on the one hand, it increases the safety region where grids can operate without withstanding systemic failures; on the other hand, it increases the possibility of a joint systems’ failure.
Graphical abstract
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 29 October 2015
- High-order control for symplectic maps
- Abstract: Publication date: Available online 30 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): M. Sansottera, A. Giorgilli, T. Carletti
We revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behavior of the map using the invariant function for the normalized map. Finally, we discuss how control terms of different orders may be introduced so as to increase the size of the stable domain of the map. The numerical examples are worked out on a two dimensional map of Hénon type.
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 30 October 2015
- On an evolution equation in a cell motility model
- Abstract: Publication date: Available online 1 November 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Matthew S. Mizuhara, Leonid Berlyand, Volodymyr Rybalko, Lei Zhang
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and net motion. This issue can be addressed both qualitatively and quantitatively by studying the evolution equation of the sharp interface limit for this system. However, this equation is non-linear and non-local and existence of solutions presents a significant analytical challenge. We establish existence of solutions for a wide class of initial data in the so-called subcritical regime. Existence is proved in a two step procedure. First, for smooth ( H 2 ) initial data we use a regularization technique. Second, we consider non-smooth initial data that are more relevant from the application point of view. Here, uniform estimates on the time when solutions exist rely on a maximum principle type argument. We also explore the long time behavior of the model using both analytical and numerical tools. We prove the nonexistence of traveling wave solutions with nonzero velocity. Numerical experiments show that presence of non-linearity and asymmetry of the initial curve results in a net motion which distinguishes it from classical volume preserving curvature motion. This is done by developing an algorithm for efficient numerical resolution of the non-local term in the evolution equation.
PubDate: 2015-11-02T05:44:31Z
- Abstract: Publication date: Available online 1 November 2015
- Minimal topological chaos coexisting with a finite set of homoclinic and
periodic orbits- Abstract: Publication date: Available online 24 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Valentín Mendoza, Walter Huaraca
In this note we explain how to find the minimal topological chaos relative to finite set of homoclinic and periodic orbits. The main tool is the pruning method, which is used for finding a hyperbolic map, obtained uncrossing pieces of the invariant manifolds, whose basic set contains all orbits forced by the finite set under consideration. Then we will show applications related to transport phenomena and to the problem of determining the orbits structure coexisting with a finite number of periodic orbits arising from the bouncing ball model.
PubDate: 2015-10-29T05:37:53Z
- Abstract: Publication date: Available online 24 October 2015
- Simple model of cell crawling
- Abstract: Publication date: Available online 24 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): T. Ohta, M. Tarama, M. Sano
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of the cell on a substrate. For time-independent forces we show that not only a stationary motion but also a limit cycle oscillation of the migration velocity and the shape occurs as a result of nonlinear coupling between different deformation modes. Time-dependent forces are generated in a stochastic manner by utilizing the so-called coherence resonance of an excitable system. The present coarse-grained model has a flexibility that it can be applied, e.g., both to keratocyte cells and to Dictyostelium cells, which exhibit quite different dynamics from each other. The key factors for the motile behavior inherent in each cell type are identified in our model.
PubDate: 2015-10-29T05:37:53Z
- Abstract: Publication date: Available online 24 October 2015
- Mixed dynamics in a parabolic standard map
- Abstract: Publication date: Available online 24 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): L.M. Lerman, J.D. Meiss
We use numerical and analytical tools to provide arguments in favor of the existence of a family of smooth, symplectic diffeomorphisms of the two-dimensional torus that have both a positive measure set with positive Lyapunov exponent and a positive measure set with zero Lyapunov exponent. The family we study is the unfolding of an almost-hyperbolic diffeomorphism on the boundary of the set of Anosov diffeomorphisms, proposed by Lewowicz.
PubDate: 2015-10-29T05:37:53Z
- Abstract: Publication date: Available online 24 October 2015
- Poincaré inverse problem and torus construction in phase space
- Abstract: Publication date: Available online 26 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Teemu Laakso, Mikko Kaasalainen
The phase space of an integrable Hamiltonian system is foliated by invariant tori. For an arbitrary Hamiltonian H such a foliation may not exist, but we can artificially construct one through a parameterised family of surfaces, with the intention of finding, in some sense, the closest integrable approximation to H . This is the Poincaré inverse problem (PIP). In this paper, we review the available methods of solving the PIP and present a new iterative approach which works well for the often problematic thin orbits.
PubDate: 2015-10-29T05:37:53Z
- Abstract: Publication date: Available online 26 October 2015
- Approaches to myosin modelling in a two-phase flow model for cell motility
- Abstract: Publication date: Available online 21 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): L.S. Kimpton, J.P. Whiteley, S.L. Waters, J.M. Oliver
A wide range of biological processes rely on the ability of cells to move through their environment. Mathematical models have been developed to improve our understanding of how cells achieve motion. Here we develop models that explicitly track the cell’s distribution of myosin within a two–phase flow framework. Myosin is a small motor protein which is important for contracting the cell’s actin cytoskeleton and enabling cell motion. The two phases represent the actin network and the cytosol in the cell. We start from a fairly general description of myosin kinetics, advection and diffusion in the two-phase flow framework, then identify a number of sub–limits of the model that may be relevant in practice, two of which we investigate further via linear stability analyses and numerical simulations. We demonstrate that myosin–driven contraction of the actin network destabilises a stationary steady state leading to cell motion, but that rapid diffusion of myosin and rapid unbinding of myosin from the actin network are stabilising. We use numerical simulation to investigate travelling–wave solutions relevant to a steadily gliding cell and we consider a reduction of the model in which the cell adheres strongly to the substrate on which it is crawling. This work demonstrates that a number of existing models for the effect of myosin on cell motility can be understood as different sub–limits of our two–phase flow model.
PubDate: 2015-10-25T05:31:47Z
- Abstract: Publication date: Available online 21 October 2015
- Clustering of extreme events created by multiple correlated maxima
- Abstract: Publication date: Available online 22 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Davide Azevedo, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas, Fagner B. Rodrigues
We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at multiple points with special emphasis for the case where these maximal points are correlated or bound by belonging to the same orbit of a certain chosen point. These multiple correlated maxima can be seen as a new mechanism creating clustering of extreme observations, i.e., the occurrence of several extreme observations concentrated in the time frame. We recall that clustering was intimately connected with periodicity when the maximum was achieved at a single point. We will study this mechanism for creating clustering and will address the existence of limiting Extreme Value Laws, the repercussions on the value of the Extremal Index, the impact on the limit of Rare Events Points Processes, the influence on clustering patterns and the competition of domains of attraction. We also consider briefly and for comparison purposes multiple uncorrelated maxima. The systems considered include expanding maps of the interval such as Rychlik maps but also maps with an indifferent fixed point such as Manneville-Pommeau maps.
PubDate: 2015-10-25T05:31:47Z
- Abstract: Publication date: Available online 22 October 2015
- Partner orbits and action differences on compact factors of the hyperbolic
plane. II: Higher-order encounters- Abstract: Publication date: Available online 22 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Hien Minh Huynh
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. We specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. The companion paper (Huynh and Kunze, 2015) proved the existence of a unique periodic partner orbit for a given periodic orbit with a small-angle self-crossing in configuration space that is a 2-encounter and derived an estimate for the action difference of the orbit pair. In this paper, we provide an inductive argument to deal with higher-order encounters: we prove that a given periodic orbit including an L -parallel encounter has ( L − 1 ) ! − 1 partner orbits; we construct partner orbits and give estimates for the action differences between orbit pairs.
PubDate: 2015-10-25T05:31:47Z
- Abstract: Publication date: Available online 22 October 2015
- Systemic risk in multiplex networks with asymmetric coupling and threshold
feedback- Abstract: Publication date: Available online 23 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Rebekka Burkholz, Matt V. Leduc, Antonios Garas, Frank Schweitzer
We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the two-layer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business and a more risky subsidiary business. In most cases, this may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach.
PubDate: 2015-10-25T05:31:47Z
- Abstract: Publication date: Available online 23 October 2015
- Positive and necklace solitary waves on bounded domains
- Abstract: Publication date: Available online 13 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): G. Fibich, D. Shpigelman
We present new solitary wave solutions of the two-dimensional nonlinear Schrödinger equation on bounded domains (such as rectangles, circles, and annuli). These multi-peak “necklace” solitary waves consist of several identical positive profiles (“pearls”), such that adjacent “pearls” have opposite signs. They are stable at low powers, but become unstable at powers well below the critical power for collapse P cr . This is in contrast with the ground-state (“single-pearl”) solitary waves on bounded domains, which are stable at any power below P cr . On annular domains, the ground state solitary waves are radial at low powers, but undergo a symmetry breaking at a threshold power well below P cr . As in the case of convex bounded domains, necklace solitary waves on the annulus are stable at low powers and become unstable at powers well below P cr . Unlike on convex bounded domains, however, necklace solitary waves on the annulus have a second stability regime at powers well above P cr . For example, when the ratio of the inner to outer radii is 1:2, four-pearl necklaces are stable when their power is between 3.1 P cr and 3.7 P cr . This finding opens the possibility to propagate localized laser beams with substantially more power than was possible until now. The instability of necklace solitary waves is excited by perturbations that break the antisymmetry between adjacent pearls, and is manifested by power transfer between pearls. In particular, necklace instability is unrelated to collapse. In order to compute numerically the profile of necklace solitary waves on bounded domains, we introduce a non-spectral variant of Petviashvili’s renormalization method.
PubDate: 2015-10-20T12:15:53Z
- Abstract: Publication date: Available online 13 October 2015
- Oscillations and uniaxial mechanochemical waves in a model of an active
poroelastic medium: Application to deformation patterns in protoplasmic
droplets of Physarum polycephalum- Abstract: Publication date: Available online 13 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Sergio Alonso, Ulrike Strachauer, Markus Radszuweit, Markus Bär, Marcus J.B. Hauser
Self-organization in cells often manifests itself in oscillations and waves. Here, we address deformation waves in protoplasmic droplets of the plasmodial slime mold Physarum polycephalum by modelling and experiments. In particular, we extend a one-dimensional model that considered the cell as an poroelastic medium, where active tension caused mechanochemical waves that were regulated by an inhibitor (M. Radszuweit et al., 2013). Our extension consists of a simple, qualitative chemical reaction-diffusion model (Brusselator) that describes the regulation of the inhibitor by another biochemical species. The biochemical reaction enhances the formation of mechanochemical waves if the reaction rates and input concentrations are near or inside an oscillatory regime. The period of the waves is found to be controlled by the characteristic oscillation period, whereas their wavelength is set by mechanical parameters. The model also allows for a systematic study of the chemical activity at the onset of mechanochemical waves. We also present examples for pattern formation in protoplasmic droplets of Physarum polycephalum including global oscillations where the central region of the droplets is in antiphase to the boundary zone, as well as travelling and standing wave like uniaxial patterns. Finally, we apply our model to reproduce these experimental results by identifying the active tension inhibitor with the intracellular calcium concentration in the Physarum droplets and by using parameter values from mechanical experiments, respectively knowledge about the properties of calcium oscillations in Physarum. The simulation results are then found to be in good agreement with the experimental observations.
PubDate: 2015-10-20T12:15:53Z
- Abstract: Publication date: Available online 13 October 2015
- Isles within islets: The lattice origin of small-world networks in
pancreatic tissues- Abstract: Publication date: Available online 13 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Amlan K. Barua, Pranay Goel
The traditional computational model of the pancreatic islets of Langerhans is a lattice of β -cells connected with gap junctions. Numerous studies have investigated the behavior of networks of coupled β -cells and have shown that gap junctions synchronize bursting strongly. This simplistic architecture of islets, however, seems increasingly untenable at the face of recent experimental advances. In a microfluidics experiment on isolated islets, Rocheleau et al. (2004) showed a failure of penetration of excitation when one end received high glucose and other end was not excited sufficiently; this suggested that gap junctions may not be efficient at inducing synchrony throughout the islet. Recently, Stozer et al. (2013) have argued that the functional networks of β -cells in an islet are small world. Their results implicate the existence of a few long-range connections among cells in the network. The physiological reason underlying this claim is not well understood. These studies cast doubt on the original lattice model that largely predict an all-or-none synchrony among the cells. Here we have attempted to reconcile these observations in a unified framework. We assume that cells in the islet are coupled randomly to their nearest neighbors with some probability, p . We simulated detailed β -cell bursting in such islets. By varying p systematically we were led to network parameters similar to those obtained by Stozer et al. (2013). We find that the networks within islets break up into components giving rise to smaller isles within the super structure–isles-within-islets, as it were. This structure can also account for the partial excitation seen by Rocheleau et al. (2004) Our updated view of islet architecture thus explains the paradox how islets can have strongly synchronizing gap junctions, and be weakly coordinated at the same time.
PubDate: 2015-10-20T12:15:53Z
- Abstract: Publication date: Available online 13 October 2015
- Stochastic stability of measures in gradient systems
- Abstract: Publication date: Available online 9 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Wen Huang, Min Ji, Zhenxin Liu, Yingfei Yi
Stochastic stability of a compact invariant set of a finite dimensional, dissipative system is studied in our recent work “Concentration and limit behaviors of stationary measures” (Huang et al., 2015) for general white noise perturbations. In particular, it is shown under some Lyapunov conditions that the global attractor of the systems is always stable under general noise perturbations and any strong local attractor in it can be stabilized by a particular family of noise perturbations. Nevertheless, not much is known about the stochastic stability of an invariant measure in such a system. In this paper, we will study the issue of stochastic stability of invariant measures with respect to a finite dimensional, dissipative gradient system with potential function f . As we will show, a special property of such a system is that it is the set of equilibria which is stable under general noise perturbations and the set S f of global minimal points of f which is stable under additive noise perturbations. For stochastic stability of invariant measures in such a system, we will characterize two cases of f , one corresponding to the case of finite S f and the other one corresponding to the case when S f is of positive Lebesgue measure, such that either some combined Dirac measures or the normalized Lebesgue measure on S f is stable under additive noise perturbations. However, we will show by constructing an example that such measure stability can fail even in the simplest situation, i.e., in 1 -dimension there exists a potential function f such that S f consists of merely two points but no invariant measure of the corresponding gradient system is stable under additive noise perturbations. Crucial roles played by multiplicative and additive noise perturbations to the measure stability of a gradient system will also be discussed. In particular, the nature of instabilities of the normalized Lebesgue measure on S f under multiplicative noise perturbations will be exhibited by an example.
PubDate: 2015-10-11T17:52:05Z
- Abstract: Publication date: Available online 9 October 2015
- Radial symmetry on three-dimensional shells in the Landau-de Gennes theory
- Abstract: Publication date: Available online 9 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Giacomo Canevari, Mythily Ramaswamy, Apala Majumdar
We study the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We prove that the radial-hedgehog solution is the unique minimizer of the Landau-de Gennes energy in two separate regimes: (i) for thin shells when the temperature is below the critical nematic supercooling temperature and (ii) for a fixed shell width at sufficiently low temperatures. In case (i), we provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution.
PubDate: 2015-10-11T17:52:05Z
- Abstract: Publication date: Available online 9 October 2015
- Stratification and enumeration of Boolean functions by canalizing depth
- Abstract: Publication date: Available online 8 October 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Qijun He, Matthew Macauley
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively “picked off”, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canalizing functions, and it yields a stratification of all Boolean functions by their canalizing depth. As a result, we obtain closed formulas for the number of n -variable Boolean functions with depth k , which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.
PubDate: 2015-10-11T17:52:05Z
- Abstract: Publication date: Available online 8 October 2015
- Large-scale weakly nonlinear perturbations of convective magnetic dynamos
in a rotating layer- Abstract: Publication date: Available online 30 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): R. Chertovskih, V. Zheligovsky
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the α -effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer of incompressible electrically conducting fluid that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in the expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetries of the perturbed state are now missing. Numerical results for the amplitude equations show that a large-scale perturbation, periodic in slow horizontal variable, either converges to a short-scale neutral stability mode with amplitudes tending to constant values, or it blows up at a finite slow time.
PubDate: 2015-10-03T18:52:10Z
- Abstract: Publication date: Available online 30 September 2015
- Membrane tension feedback on shape and motility of eukaryotic cells
- Abstract: Publication date: Available online 25 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Benjamin Winkler, Igor S. Aranson, Falko Ziebert
In the framework of a phase field model of a single cell crawling on a substrate, we investigate how the properties of the cell membrane affect the shape and motility of the cell. Since the membrane influences the cell dynamics on multiple levels and provides a nontrivial feedback, we consider the following fundamental interactions: (i) the reduction of the actin polymerization rate by membrane tension; (ii) area conservation of the cell’s two-dimensional cross-section vs. conservation of the circumference (i.e. membrane inextensibility); and (iii) the contribution from the membrane’s bending energy to the shape and integrity of the cell. As in experiments, we investigate two pertinent observables—the cell’s velocity and its aspect ratio. We find that the most important effect is the feedback of membrane tension on the actin polymerization. Bending rigidity has only minor effects, visible mostly in dynamic reshaping events, as exemplified by collisions of the cell with an obstacle.
PubDate: 2015-09-25T18:33:46Z
- Abstract: Publication date: Available online 25 September 2015
- Asymptotic analysis of a viscous thread extending under gravity
- Abstract: Publication date: Available online 21 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Jonathan J. Wylie, Huaxiong Huang, Robert M. Miura
Despite extensive research on extensional flows, there is no complete explanation for why highly viscous fluids extending under gravity can form such persistent and stable filaments with no sign of destabilization from surface tension. We therefore investigate the motion of a slender axisymmetric viscous thread that is supported at its top by a fixed horizontal surface and extends downward under gravity. In the case in which inertia and surface tension are initially negligible, we consider the long-wavelength equations for the full initial-boundary-value problem for a thread of arbitrary initial shape. We show that, eventually, the accelerations in the thread become sufficiently large that the inertial terms become important. Thus, we keep the inertial terms and, using matched asymptotic expansions, obtain solutions for the full initial-boundary-value problem. We show that the dynamics can be divided into two generic cases that exhibit very different behaviour. In the first case, the thread develops a long thin region that joins together two fluid masses. In this case, we use order-of-magnitude estimates to show that surface-tension-driven pinching will not occur if the square root of the Reynolds number is much greater than the initial aspect ratio divided by the Bond number. In the second case, the thread becomes thin near the horizontal surface. In this case, we show that the long-wavelength equations will ultimately break down and discuss the role of inertia in determining the dynamics. The asymptotic procedures require a number of novel techniques and the resulting solutions exhibit surprisingly rich behavior. The solution allows us to understand the mechanisms that underlie highly persistent filaments.
PubDate: 2015-09-25T18:33:46Z
- Abstract: Publication date: Available online 21 September 2015
- The effects of wind and nonlinear damping on rogue waves and permanent
downshift- Abstract: Publication date: Available online 21 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): C.M. Schober, M. Strawn
In this paper we investigate the effects of wind and nonlinear damping on permanent downshift and the formation of rogue waves in the framework of a HONLS model. Wind effects are incorporated by including a uniform linear damping/forcing term in the model. The strength of the wind, Γ , is allowed to vary as well as wind duration. Determining permanent downshift is not straightforward and we propose a criteria for permanent downshift related to our numerical experiments. We consider large ensembles of initial data for modulated unstable Stokes waves with N = 1 , 2 , 3 unstable modes. In the nonlinear damped HONLS evolution we find permanent downshift is observed whenever the strength of the nonlinear damping β > 0.1 . Notably, rogue waves typically do not develop after the time of permanent downshift, implying that a downshifted sea-state does not allow for any further rogue waves. Incorporating wind effects into the nonlinear damped HONLS model, we find that damping by the wind weakens downshifting while forcing by the wind enhances downshifting. The proximity of the initial data to unstable plane waves impacts the characteristic features of the rogue waves in the nonlinear damped HONLS evolution. We find that as the initial data is chosen closer to the plane wave, the maximum strength, number, and lifetime of rogue waves increase while the time of permanent downshift decreases. Alternatively, we show that the greater the wave strength, the more rogue waves, or the longer their lifetime, the earlier permanent downshift occurs.
PubDate: 2015-09-25T18:33:46Z
- Abstract: Publication date: Available online 21 September 2015
- Exact solutions of the Hirota equation and vortex filaments motion
- Abstract: Publication date: Available online 21 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): F. Demontis, G. Ortenzi, C. van der Mee
By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N -soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.
PubDate: 2015-09-25T18:33:46Z
- Abstract: Publication date: Available online 21 September 2015
- Singularity confinement and full-deautonomisation: A discrete
integrability criterion- Abstract: Publication date: Available online 14 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): B. Grammaticos, A. Ramani, R. Willox, T. Mase, J. Satsuma
We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions of a given discrete system obtained by adding terms that are initially absent, but whose presence does not alter the singularity pattern. A justification for this approach is given through an algebro-geometric analysis. We also introduce the notions of early and late confinement. While the former is a confinement that may exist already for the autonomous system, the latter corresponds to a singularity pattern longer than that of the autonomous case. Late confinement will be shown to play an important role in the singularity analysis of systems with non-trivial gauge freedom, for which the existence of an undetected gauge in conjunction with a sketchy analysis, might lead to erroneous conclusions as to their integrability. An algebro-geometric analysis of the role of late confinement in this context is also offered. This novel type of singularity confinement analysis will be shown to allow for the exact calculation of the algebraic entropy of a given mapping.
PubDate: 2015-09-18T07:48:29Z
- Abstract: Publication date: Available online 14 September 2015
- Numerical analysis of the subcritical feature of electro-thermo-convection
in a plane layer of dielectric liquid- Abstract: Publication date: Available online 11 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Jian Wu, Philippe Traoré, Alberto T. Pérez, Mengqi Zhang
This paper reports a numerical investigation with a horizontal layer of dielectric liquid subjected to the simultaneous effects of external thermal and electric fields. The flow is driven by the buoyancy force and the Coulomb force, which depend on the Rayleigh number (Ra) and the electric Rayleigh number ( T ), respectively. We consider a strong unipolar injection from the lower electrode and a destabilizing thermal gradient. The two driving forces cooperate with each other in destabilizing the system. The neutral stability curve in the Ra– T plane is successfully reproduced from the direct numerical results, and it is shown to be independent on the Prandtl number (Pr) and the dimensionless mobility number ( M ). On the other hand, both the bifurcation types of the linear instability (subcritical or supercritical) and the finite amplitude stability criterion depend strongly on the combination of Pr and M .
PubDate: 2015-09-14T07:41:12Z
- Abstract: Publication date: Available online 11 September 2015
- Predictability of threshold exceedances in dynamical systems
- Abstract: Publication date: Available online 10 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Tamás Bódai
In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events–the cornerstone also for the categoric (as opposed to probabilistic) prediction of threshold exceedences–is established from long time series of one or more observables of the same system. The prediction skill is measured by a summary index of the ROC curve that relates the hit- and false alarm rates. Our results for the examined systems suggest that exceedances of higher thresholds are more predictable; or in other words: rare large magnitude, i.e., extreme, events are more predictable than frequent typical events. We find this to hold provided that the bin size for binning time series data is optimized, but not necessarily otherwise. This can be viewed as a confirmation of a counterintuitive (and seemingly contrafactual) statement that was previously formulated for more simple autoregressive stochastic processes. However, we argue that for dynamical systems in general it may be typical only, but not universally true. We argue that when there is a sufficient amount of data depending on the precision of observation, the skill of a class of data-driven categoric predictions of threshold exceedences approximates the skill of the analogous model-driven prediction, assuming strictly no model errors. Therefore, stronger extremes in terms of higher threshold levels are more predictable both in case of data- and model-driven prediction. Furthermore, we show that a quantity commonly regarded as a measure of predictability, the finite-time maximal Lyapunov exponent, does not correspond directly to the ROC-based measure of prediction skill when they are viewed as functions of the prediction lead time and the threshold level. This points to the fact that even if the Lyapunov exponent as an intrinsic property of the system, measuring the instability of trajectories, determines predictability, it does that in a nontrivial manner.
PubDate: 2015-09-14T07:41:12Z
- Abstract: Publication date: Available online 10 September 2015
- Spectral transverse instabilities and soliton dynamics in the higher-order
multidimensional nonlinear Schrödinger equation- Abstract: Publication date: Available online 11 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Justin T. Cole, Ziad H. Musslimani
Spectral transverse instabilities of one-dimensional solitary wave solutions to the two-dimensional nonlinear Schrödinger (NLS) equation with fourth-order dispersion/diffraction subject to higher-dimensional perturbations are studied. A linear boundary value problem governing the evolution of the transverse perturbations is derived. The eigenvalues of the perturbations are numerically computed using Fourier and finite difference differentiation matrices. It is found that for both signs of the higher-order dispersion coefficient there exists a finite band of unstable transverse modes. In the long wavelength limit we derive an asymptotic formula for the perturbation growth rate that agrees well with the numerical findings. Using a variational formulation based on Lagrangian model reduction, an approximate expression for the perturbation eigenvalues is obtained and its validity is compared with both the asymptotic and numerical results. The time dynamics of a one-dimensional soliton stripe in the presence of a transverse perturbation is studied using direct numerical simulations. Numerical nonlinear stability analysis is also addressed.
PubDate: 2015-09-14T07:41:12Z
- Abstract: Publication date: Available online 11 September 2015
- Three-dimensional forced-damped dynamical systems with rich dynamics:
Bifurcations, chaos and unbounded solutions- Abstract: Publication date: Available online 9 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Tomoyuki Miyaji, Hisashi Okamoto, Alex D.D. Craik
We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
PubDate: 2015-09-10T07:33:26Z
- Abstract: Publication date: Available online 9 September 2015
- Experiments on a non-smoothly-forced oscillator
- Abstract: Publication date: Available online 9 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Lawrence N. Virgin, Christopher George, Ashwath Kini
This paper describes some typical behavior encountered in the response of a harmonically-excited mechanical system in which a severe nonlinearity occurs due to an impact. Although such systems have received considerable recent attention (most of it from a theoretical viewpoint), the system scrutinized in this paper also involves a discrete input of energy at the impact condition. That is, it is kicked when contact is made. One of the motivations for this work is related to a classic pinball machine in which a ball striking a bumper experiences a sudden impulse, introducing additional unpredictability to the motion of the ball. A one-dimensional analog of a pinball machine was the subject of a detailed mathematical study in Pring and Budd (2011), and the current paper details behavior obtained from a mechanical experiment and describes dynamics not observed in a conventional (passive) impact oscillator.
PubDate: 2015-09-10T07:33:26Z
- Abstract: Publication date: Available online 9 September 2015
- Dispersive shock waves in nematic liquid crystals
- Abstract: Publication date: Available online 3 September 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Noel F. Smyth
The propagation of coherent light with an initial step intensity profile in a nematic liquid crystal is studied using modulation theory. The propagation of light in a nematic liquid crystal is governed by a coupled system consisting of a nonlinear Schrödinger equation for the light beam and an elliptic equation for the medium response. In general, the intensity step breaks up into a dispersive shock wave, or undular bore, and an expansion fan. In the experimental parameter regime for which the nematic response is highly nonlocal, this nematic bore is found to differ substantially from the standard defocusing nonlinear Schrödinger equation structure due to the effect of the nonlocality of the nematic medium. It is found that the undular bore is of Korteweg-de Vries equation-type, consisting of bright waves, rather than of nonlinear Schrödinger equation-type, consisting of dark waves. In addition, ahead of this Korteweg-de Vries bore there can be a uniform wavetrain with a short front which brings the solution down to the initial level ahead. It is found that this uniform wavetrain does not exist if the initial jump is below a critical value. Analytical solutions for the various parts of the nematic bore are found, with emphasis on the role of the nonlocality of the nematic medium in shaping this structure. Excellent agreement between full numerical solutions of the governing nematicon equations and these analytical solutions is found.
PubDate: 2015-09-05T18:05:47Z
- Abstract: Publication date: Available online 3 September 2015
- Numerical and experimental observation of Arnol’d resonance webs in
an electrical circuit- Abstract: Publication date: Available online 31 August 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Naohiko Inaba, Kyohei Kamiyama, Takuji Kousaka, Tetsuro Endo
An extensive bifurcation analysis of partial and complete synchronizations of three-frequency quasi-periodic oscillations generated in an electric circuit is presented. Our model uses two-coupled hysteresis oscillators and a rectangular wave forcing term. The governing equation of the circuit is represented by a piecewise-constant dynamics generating a three-dimensional torus. The Lyapunov exponents are precisely calculated using explicit solutions without numerically solving any implicit equation. By analyzing this extremely simple circuit, we clearly demonstrate that it generates an extremely complex bifurcation structure called Arnol’d resonance web. Inevitably, chaos is observed in the neighborhood of Chenciner bubbles around which regions generating three-dimensional tori emanate. Furthermore, the numerical results are experimentally verified.
PubDate: 2015-08-31T19:27:50Z
- Abstract: Publication date: Available online 31 August 2015
- Cellular non-deterministic automata and partial differential equations
- Abstract: Publication date: Available online 11 August 2015
Source:Physica D: Nonlinear Phenomena
Author(s): D. Kohler, J. Müller, U. Wever
We define cellular non-deterministic automata (CNDA) in the spirit of non-deterministic automata theory. They are different from the well-known stochastic automata. We propose the concept of deterministic superautomata to analyze the dynamical behavior of a CNDA and show especially that a CNDA can be embedded in a deterministic cellular automaton. As an application we discuss a connection between certain partial differential equations and CNDA.
PubDate: 2015-08-15T04:48:40Z
- Abstract: Publication date: Available online 11 August 2015
- A computational study of residual KPP front speeds in time-periodic
cellular flows in the small diffusion limit- Abstract: Publication date: Available online 7 August 2015
Source:Physica D: Nonlinear Phenomena
Author(s): Penghe Zu, Long Chen, Jack Xin
The minimal speeds ( c ∗ ) of the Kolmogorov-Petrovsky-Piskunov (KPP) fronts at small diffusion ( ϵ ≪ 1 ) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c ∗ reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advection-diffusion operator with space-time periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c ∗ = O ( ϵ 1 / 4 ) in steady cellular flows, a new relation c ∗ = O ( 1 ) as ϵ ≪ 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub-diffusion process.
PubDate: 2015-08-10T04:29:17Z
- Abstract: Publication date: Available online 7 August 2015